C. Gavoille, M. Katz, N.A. Katz, C. Paul, D. Peleg, Approximate Distance Labeling Schemes, Proc. 9th Ann. European Symp. Algorithms (ESA  Home/Search   Document Details and Download   Summary   Related Articles   Check

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Cyril Gavoille, Michal Katz, Nir A. Katz, Christophe Paul, and David Peleg. Approximate distance labeling schemes. Research Report RR-1250-00, LaBRI, University of Bordeaux, 351, cours de la Liberation, 33405 Talence Cedex, France, December 2000.

....and the tree length can be large. For instance, a p q mesh (p rows, q columns) has chordality pq) However, Theorem 2 The tree length of the mesh with p rows and q columns is p 1 if p = q is odd, or is minfp; qg otherwise. However chordality is an upper bound for the tree length: Theorem 3 [6] Every k chordal graph has tree length at most k=2. 3 Optimal tree decomposition Let us de ne an optimal tree decomposition for a graph G as a treedecomposition of G whose width is at most k and whose length is at most , where k and are respectively the tree width and the tree length of G. ....

C. Gavoille, M. Katz, N. A. Katz, C. Paul, and D. Peleg, Approximate distance labeling schemes, in ESA, vol. 2161 of LNCS, Springer, Aug. 2001, pp. 476-488.

....The time to decode the estimated distance is O( This implies a (2 log n; 0) approximate scheme n) bit labels for general unweighted graphs. These results are complemented by a lower bound in ) on the label size of ( Omega ( 0) approximate schemes, presented independently in [120] and in [60]. It is interesting to notice that a small variation on the quality of the estimators, say, moving from (1; 0) approximate to (1 o(1) 0) approximate or to (1; O(1) approximate schemes, results in a significant impact on the label size. Trees, and more generally graphs with r(n) separators, ....

....say, moving from (1; 0) approximate to (1 o(1) 0) approximate or to (1; O(1) approximate schemes, results in a significant impact on the label size. Trees, and more generally graphs with r(n) separators, support a (1 1= log n; 0) approximate scheme with O(R(n) Deltalog log n) bit labels [60]. In particular, trees enjoy O(log n Delta log log n) bit label (1 1= log n; 0) approximate distance labeling scheme. A lower bound of Omega (log n Delta log log n) is also shown in [60] for any (1 1= log n; 0) approximate distance labeling scheme on the class of trees. However, distances ....

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C. Gavoille, M. Katz, N.A. Katz, C. Paul, and D. Peleg. Approximate distance labeling schemes. In European Symp. on Algorithms, Aug. 2001.

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Cyril Gavoille, Michal Katz, Nir A. Katz, Christophe Paul, and David Peleg. Approximate distance labeling schemes. Research Report RR-1250-00, LaBRI, University of Bordeaux, 351, cours de la Liberation, 33405 Talence Cedex, France, December 2000.

....upper and lower bounds for these two latter results. The upper bound for planar graphs is O( n log n) coming from a more general result about graphs having small separators. Related works concern distance labeling schemes in dynamic tree networks [22] and approximate distance labeling schemes [12,27,28]. Several ecient schemes have been designed for speci c graph families: interval and permutation graphs [21] distance hereditary graphs [13] bounded tree width graphs (or graphs with bounded vertex separator) and more generally bounded clique width graphs [9] All support an O(log ....

C. Gavoille, M. Katz, N. A. Katz, C. Paul, and D. Peleg, Approximate distance labeling schemes, in 9 European Symp. on Algorithms (ESA), vol. 2161 of LNCS, Springer, 2001, pp. 476-488.

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Cyril Gavoille, Michal Katz, Nir A. Katz, Christophe Paul, and David Peleg. Approximate distance labeling schemes. In F. Meyer auf der Heide, editor, 9 Annual European Symposium on Algorithms (ESA), volume 2161 of Lecture Notes in Computer Science, pages 476-488. Springer, August 2001.

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C. Gavoille, M. Katz, N.A. Katz, C. Paul, and D. Peleg. Approximate distance labeling schemes. In 9 Annual European Symposium on Algorithms (ESA), volume 2161 of Lecture Notes in Computer Science, pages 476-488. Springer, August 2001.

....using the corresponding labels. Other functions can be computed by suitable labeling schemes: ancestry and small distances in trees [2, 20, 21] near common ancestor in trees [1] and other functions [22, 26] A recent overview on compact labeling schemes can be founded in [14] De nition 1. 1 ([13]) Given a family F of connected graphs, an (s; r) approximate distance labeling scheme on F , s; r) approximate DLS for short, is a pair hL; fi, where L is call the labeling function and f the distance decoder, such that for any G 2 F and any pair x; y of distinct vertices of G, L(x; G) 2 f0; ....

....operations on O(log n) bit words in constant time. We show how the split decomposition of a graph [11] can be used to design ecient labeling schemes. Our technique allows to combine di erent types of schemes. Applying this technique, we show that the optimal schemes for trees obtained by [13, 15] can be generalized to distance hereditary graphs. Our results are extended to other classical families of graphs. The paper is organized as follows. Section 2 presents how the split decomposition can be used to compute an tree like auxiliary graph in which the distances in the original graph can ....

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C. Gavoille, M. Katz, N. A. Katz, C. Paul, and D. Peleg, Approximate distance labeling schemes, in 9 Annual European Symposium on Algorithms (ESA), vol. 2161 of Lecture Notes in Computer Science, Springer, Aug. 2001, pp. 476-488.

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Cyril Gavoille, Michal Katz, Nir A. Katz, Christophe Paul, and David Peleg. Approximate distance labeling schemes. Research Report RR-1250-00, LaBRI, University of Bordeaux, 351, cours de la Liberation, 33405 Talence Cedex, France, December 2000.

....G. The datastructure consists in a label L(x; G) assigned to each vertex x of G such that the distance dG (x; y) between any two vertices x and y can be estimated as a function f(L(x; G) L(y; G) Two problems can be considered: exact distance labelling [4] and approximate distance labelling [3]. In the further one, we look for an exact value of the distance while in the later one, we estimate the distance within a multiplicative factor s 1 and or with an additive constant r 0 (i.e. dG (x; y) 6 f(L(x; G) L(y; G) 6 s dG (x; y) r ) We are interested in nding labelling scheme ....

....is replaced by the edges of weight 1=2, the distances leave unchanged. Given an integer W 0, let us denote by W tree any weighted tree whose edge cost is a non null integer, and such that the weighted diameter is at most W . We need the following result to complete our result. Lemma 2 ([3]) There exists a (1 1= log W ) multiplicative (resp. exact) distance labelling scheme using labels of size O(log n log log W ) bits (resp. O(log n log W ) bits) for the family of W trees with at most n vertices. Moreover the scheme is polynomial time constructible, and under a word RAM model ....

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Cyril Gavoille, Michal Katz, Nir A. Katz, Christophe Paul, and David Peleg. Approximate distance labeling schemes. Research Report RR-1250-00, LaBRI, University of Bordeaux, 351, cours de la Liberation, 33405 Talence Cedex, France, December 2000.

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C. Gavoille, M. Katz, N.A. Katz, C. Paul, D. Peleg, Approximate Distance Labeling Schemes, Proc. 9th Ann. European Symp. Algorithms (ESA

No context found.

C. Gavoille, M. Katz, N. A. Katz, C. Paul, and D. Peleg. Approximate distance labeling schemes. TR RR-1250-00, LaBRI, University of Bordeaux, 351, cours de la Liberation, 33405 Talence Cedex, France, Dec. 2000.

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